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Table 4 A summary of the estimation results for the parameters Θ

From: Tie-formation process within the communities of the Japanese production network: application of an exponential random graph model

Attributes \(\overline {\Theta }_{MLE}\) \(\Theta _{MLE}^{max}\) \(\Theta _{MLE}^{min}\) s.d. (ΘMLE) nonsig. positive negative
Endogenous attributes:        
Reciprocity 1.59 3.78 -2.62 1.31 15% 80% 5%
Popularity (k-in-stars) 3.68 8.25 0.90 1.79 8% 92% 0%
Activity (k-out-stars) -1.48 -0.66 -4.32 0.81 14% 0% 86%
k-two-paths -0.01 0.41 -1.00 0.15 60% 28% 12%
Cyclic closure (AT-C) -0.06 0.56 -2.14 0.26 59% 10% 31%
Path closure (AT-T) 0.00 0.31 -1.38 0.24 48% 40% 12%
Activity closure (AT-U) -0.09 0.35 -1.58 0.40 39% 37% 24%
Popularity closure (AT-D) -0.28 0.31 -3.38 0.51 50% 6% 44%
Exogenous attributes:        
Sector homophily 0.19 2.58 -0.43 0.45 41% 42% 17%
Location homophily 0.86 3.68 0.13 0.72 9% 91% 0%
Bank homophily 0.44 0.14 3.12 0.002 15% 80% 5%
Size heterophily 3.04·10−4 9.02·10−3 -6.15. 10−03 1.12·10−03 48% 33% 19%
Sales heterophily 3.59·10−8 5.31·10−7 4.31. 10−10 7.26·10−08 21% 79% 0%
Sales receiver effect 5.80·10−8 1.22·10−6 4.73. 10−10 1.50·10−07 22% 78% 0%
Sales sender effect − 1.31·10−8 − 1.18·10−10 -3.37. 10−07 3.71·10−08 52% 0% 48%
  1. The results for each parameter are given based on the 100 considered communities in the Japanese production network. A parameter is considered significant for a Wald ratio of ≥ 2. Significance is rejected for a Wald ratio of < 2. The entry in the significance column (sig.) is + if the parameter is significant and otherwise